Here's the thrust of King's argument divided into four points. The
quotes I have used are from the text of the Washington speech at
http://web66.coled.umn.edu/new/MLK/MLK.html . The quotes are intended
as markers, so that you can see which sections of the speech I am
"In a sense we have come to our nation's capital to cash a check."
In other words, the black community is owed liberation. Lincoln's
Emancipation Declaration promised freedom for slaves, but "the Negro
is still not free" and further liberation and rights are necessary.
"We must forever conduct our struggle on the high plane of dignity and
discipline... we cannot walk alone."
King is careful to stress his non-violent beliefs. While the struggle
is just, it should not deteriorate into violence. This is because the
black community should not seek to alienate the white community.
"Their freedom is inextricably bound to our freedom," and a common
solution should be sought.
"I say to you today, my friends, that in spite of the difficulties and
frustrations of the moment, I still have a dream."
King stresses the importance of hope. This is the most famous and
moving part of the speech. King recognises that many of his audience
have suffered persecution and violence, but that they must have hope
and faith that the "promised land" of complete integration will happen
"If America is to be a great nation this must become true."
King stresses that this is not just a problem for the black community,
but for all Americans. King uses the words of "My country, 'tis of
thee" to stress the national, even patriotic importance of the
struggle, repeating the line "Let freedom ring" to link the civil
rights struggle with the ideals of the founding fathers.
I hope this simplifies matters for you. Please ask for clarification
if you are unsure about any of the above.